Note on a certain Cremona transformation associated with a plane triangle
Haridas Bagchi (1950)
Rendiconti del Seminario Matematico della Università di Padova
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Haridas Bagchi (1950)
Rendiconti del Seminario Matematico della Università di Padova
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Čerin, Zvonko (2000)
Mathematica Pannonica
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Albert Dou (1992)
Publicacions Matemàtiques
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This "Corolarium" of the (1733) contains an original proof of propositions 1.27 and 1.28 of Euclide's . In the same corollary Saccheri explains why he dispenses "not only with the propositions 1.27 and 1.28, but also with the very propositions 1.16 and 1.17, except when it is clearly dealt with a triangle circumscribed by alls sides"; and also why he rejects Euclide's proof. Moreover the corollarium has implications for confirmation of Saccheri's method; and also for his concept of...
Roland Coghetto (2016)
Formalized Mathematics
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We introduce, using the Mizar system [1], some basic concepts of Euclidean geometry: the half length and the midpoint of a segment, the perpendicular bisector of a segment, the medians (the cevians that join the vertices of a triangle to the midpoints of the opposite sides) of a triangle. We prove the existence and uniqueness of the circumcenter of a triangle (the intersection of the three perpendicular bisectors of the sides of the triangle). The extended law of sines and the formula...
L. Szczerba, Alfred Tarski (1979)
Fundamenta Mathematicae
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Peter Greenberg (1998)
Annales de l'institut Fourier
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To any compactly supported, area preserving, piecewise linear homeomorphism of the plane is associated a relation in of the smallest field whose elements are needed to write the homeomorphism. Using a formula of J. Morita, we show how to calculate the relation, in some simple cases. As applications, a “reciprocity” formula for a pair of triangles in the plane, and some explicit elements of torsion in of certain function fields are found.
Roland Coghetto (2014)
Formalized Mathematics
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We calculate the values of the trigonometric functions for angles: [XXX] , by [16]. After defining some trigonometric identities, we demonstrate conventional trigonometric formulas in the triangle, and the geometric property, by [14], of the triangle inscribed in a semicircle, by the proposition 3.31 in [15]. Then we define the diameter of the circumscribed circle of a triangle using the definition of the area of a triangle and prove some identities of a triangle [9]. We conclude by...
Roland Coghetto (2015)
Formalized Mathematics
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Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].
Miguel de Guzmán (2001)
RACSAM
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A simple proof is presented of a famous, and difficult, theorem by Jakob Steiner. By means of a straightforward transformation of the triangle, the proof of the theorem is reduced to the case of the equilateral triangle. Several relations of the Steiner deltoid with the Feuerbach circle and the Morley triangle appear then as obvious.
Cipu, Mihai (2004)
Acta Universitatis Apulensis. Mathematics - Informatics
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